Sample Size Algorithms in Clinical Trials
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Chien-Hua Wu, PhD Department of Applied Mathematics, Chung-Yuan Christian University, Chung-Li, Taiwan Shu-Mei Wan Department of Finance, Lunghwa University of Science and Technology, Taoyuan, Taiwan Yu-Chun Yang, MS Department of Applied Mathematics, Chung-Yuan Christian University, Chung-Li, Taiwan
Sample Size Algorithms in Clinical Trials
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Given the general difficulty of working out an exact answer or a good approximation algebraically, it would be useful to have an alternative approach that is simple to use to estimate the sample size of study planning. With the speed of modern computers it is now feasible to replace approximations with algorithm methods. The method that we introduce in this article is an extremely powerful tool that is used internally by a computer program to calculate the sample sizes of various tests.
Chiung-Yu Huang, MS Department of Applied Mathematics, Chung-Yuan Christian University, Chung-Li, Taiwan
Key Words Two-sample t test; ANOVA; Chi-square; Binomial; Matched pair; Superiority; Noninferiority; Equivalence; Sample size algorithm; Fisher’s exact test Correspondence Address Chien-Hua Wu, PhD, Assistant Professor, Department of Applied Mathematics, Chung-Yuan Christian University, ChungLi, Taiwan 32023 (email: [email protected]).
INTRODUCTION When planning a clinical trial, it is very important to consider how many participants we will need to reliably answer the clinical question. Too many participants are a needless waste of resources. Too few participants will not produce a precise, reliable, and definitive answer. An investigator must strike a balance between enrolling sufficient patients to detect important differences, but not so many patients that he would unnecessarily waste important resources. Thus, to provide an accurate and reliable sample size, an appropriate method of sample size determination is desirable. There is a vast literature providing exact and approximate sample size formulas or power functions for specific problems. A few general references are Chow, Shao, and Wang (1), Cohen (2), Desu and Raghavarao (3), and Lachin (4). Given the general difficulty of working out an exact answer or a good approximation algebraically, it would be useful, particularly when faced with a new or nonstandard situation, to have an alternative approach that is simple to use yet versatile enough to give an exact solution for a broad range of problems. With the current availability of inexpensive high-speed computing, the proposed procedure is suggested as another computer approach.
METHOD Let us assume that the experiment is being performed to test a null hypothesis H0 and then the sample size is to be determined so that the test has a stated amount of power at a specified alternative hypothesis Ha. To answer the sample size question, one has to study the power of the test at Ha as a function of sample size and then solve, for sample size, the stochastic equation that sets the power function equal to the desired power. However, for most test statistics, the equations of sample
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